The incursion response was initiated due to large rat footprints being found on an ink pad which has been baited with peanut butter.
"Rats aren't particularly fussy eaters and will happily munch on eggs, chicks and even fully grown birds. New Zealand's bird population hasn't evolved with mammalian predators so they haven't developed good mechanisms for dealing with rat predation - they're sitting targets."
Ms Abbot said given the size of the rat, it was possible it swam to the island.
"Though it is also possible the rat was transported to the island on a boat which had landed without appropriate quarantine checks."
Landing on Mokoia Island requires a permit from the Mokoia Island Board of Trustees.
The only commercial operator authorised to land on the island is Kawerau Jet, who have been transporting volunteers to the island each day of the incursion.
Mokoia Island Board trustee Rawiri Bhana said the incursion would cost between $60,000 to $100,000.
"It's a huge cost and we are lucky our relationship with the Department of Conservation sees that cost taken care of because if it fell on the trust, we wouldn't be able to pay it.
"It is a very real possibility the rat could have swam from the mainland but it also could have been a stowaway on a boat that pulled in close enough to the island to have lunch.
"For us we want to see people educated because these pests are just killing machines and we want to keep the island as pristine as possible.
"We're not going to put big fences around the whole island but we do need to know if people want to go there so we can do the proper quarantine checks."
Mr Bhana said they had visited the island every day last week and are returning this week with a rodent sniffer dog.
"We are lucky to have this dog come over from Hamilton because there are only a few that go around the whole country. It is muzzled so it's no danger to the native wildlife and best case scenario it will either catch the rat or find no trace of it."
He said worse case scenario would be if the rat was pregnant.
"All we know is that it was very large, not whether it was male or female of if it could possibly be pregnant. If it is, that would be very bad for us."
The last breach was about 15 months ago.